I want to point out that the term month was originally something like MOONTH and then evolved. The reason we have a month that is not the same as a moonth is that the moon cycle is not an even number of days, and there are not an even number of moonths in a year. So, why 12 months? That goes back to the fact that there are roughly 360 days in a year, and 360 is divided nicely by 12 (BTW, the Babylonians had the year at 360 days with 5 days of partying and celebration at the end to get everything to line up again.)Would like to suggest a slang word for something important in the game. The nine week period that marks the progression of the Tournament is surely an important interval for this game. It is perhaps something like how the Indigenous Peoples of the Americas often marked the passage of time by the Moon, them and many other people worldwide. And yet, we have no name for this time marker.
Other than my ramblings here, your idea is interesting (although I think I like the Maori version better).